Modulo 2 counting of Klein-bottle leaves in smooth taut foliations

Zhang, Boyu

doi:10.2140/agt.2018.18.2701

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Modulo $2$ counting of Klein-bottle leaves in smooth taut foliations

Boyu Zhang

Algebraic & Geometric Topology 18 (2018) 2701–2727

DOI: 10.2140/agt.2018.18.2701

Abstract

We prove a modulo $2$ invariance for the number of Klein-bottle leaves in taut foliations. Given two smooth cooriented taut foliations, assume that every Klein-bottle leaf has nontrivial linear holonomy, and assume that the two foliations can be smoothly deformed to each other through taut foliations. We prove that the numbers of Klein-bottle leaves in these two foliations must have the same parity.

Keywords

taut foliations, $J$–holomorphic curves

Mathematical Subject Classification 2010

Primary: 57M50, 57R30, 57R57

References

Publication

Received: 14 March 2017

Revised: 23 March 2018

Accepted: 24 May 2018

Published: 22 August 2018

Authors

Boyu Zhang
Department of Mathematics Harvard University Cambridge, MA United States

Volume 18, issue 5 (2018)